Background

This analysis document compliments FIA NLS Models: Biomass Growth vs. Stand Age. All of the background information from that document applies to these analyses, which are extensions to them. The difference between that document and this analysis is the use of different data subsets.

Here, we fit the models using: 1) a temporally-balanced dataset, where we take the first and most-recent plot record for all plots in the dataset, 2) a temporally-balanced dataset (same as #1), but which excludes plot locations which have experienced harvest (at any point over the study interval 2000-2022)

Below the model fitting procedure is implemented by ecoprovince:

Temporally-balancing the biomass growth data set

Lets look at some quick attributes of the dataset

  • The data set has 113960 observations, comprised of 57686 plots.
  • The frequency of growth measurements among plots is as follows (n=1 through 5): 25573, 13681, 12815, 5505, 112.
  • Thus 55.67% of plots have at least two growth measurements.

Analysis 1: Temporally-balanced analysis

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4810     1461.8                                
## 2   4809     1399.7  1 62.047  213.17 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 18812.07
## 2     2 18605.23
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.2407     0.1786   1.348  0.17773    
## alpha   0.6366     0.0409  15.566  < 2e-16 ***
## a       0.0000     1.6712   0.000  1.00000    
## b       3.4218     1.6636   2.057  0.03975 *  
## c      35.4219     2.1472  16.497  < 2e-16 ***
## d       2.5909     0.7967   3.252  0.00115 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5395 on 4809 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (23 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## Warning: Removed 11 rows containing missing values (`geom_point()`).

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   9800     4156.3                                
## 2   9799     3887.7  1 268.62  677.07 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 35940.91
## 2     2 35287.81
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.28350    0.21473   5.977 2.35e-09 ***
## alpha  0.79675    0.02806  28.392  < 2e-16 ***
## a      0.33195    0.27692   1.199    0.231    
## b      2.04010    0.28037   7.276 3.69e-13 ***
## c     24.65429    0.85760  28.748  < 2e-16 ***
## d      2.38823    0.25052   9.533  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6299 on 9799 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3157 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 1573 rows containing missing values (`geom_point()`).

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5409     2038.5                                
## 2   5408     1963.5  1 74.951  206.44 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 23802.80
## 2     2 23601.98
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.36151    0.16281  -2.220  0.02643 *  
## alpha  0.70293    0.04605  15.265  < 2e-16 ***
## a      0.00000    2.13615   0.000  1.00000    
## b      4.31575    2.13643   2.020  0.04342 *  
## c     38.22036    2.84147  13.451  < 2e-16 ***
## d      2.71967    0.87701   3.101  0.00194 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6026 on 5408 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (32 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 19 rows containing missing values (`geom_point()`).

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2728     971.74                                
## 2   2727     905.51  1 66.232  199.46 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 10962.43
## 2     2 10771.51
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.19328    0.27462   0.704  0.48162    
## alpha  0.82686    0.05321  15.541  < 2e-16 ***
## a      1.32113    0.48479   2.725  0.00647 ** 
## b      2.04132    0.48660   4.195 2.81e-05 ***
## c     48.17441    4.15142  11.604  < 2e-16 ***
## d      1.97547    0.41678   4.740 2.25e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5762 on 2727 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (819 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 425 rows containing missing values (`geom_point()`).

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5252     2143.2                                
## 2   5251     2096.6  1 46.648  116.83 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 21906.12
## 2     2 21792.43
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.51043    0.14538  -3.511  0.00045 ***
## alpha  0.57800    0.05061  11.421  < 2e-16 ***
## a      2.44659    0.37027   6.608 4.29e-11 ***
## b      1.56434    0.36338   4.305 1.70e-05 ***
## c     31.40267    2.53357  12.395  < 2e-16 ***
## d      1.27701    0.27810   4.592 4.49e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6319 on 5251 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1131 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 582 rows containing missing values (`geom_point()`).

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7673     3589.5                                
## 2   7672     3215.8  1 373.72  891.59 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 38236.36
## 2     2 37394.22
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.52751    0.20834   7.332  2.5e-13 ***
## alpha  0.88547    0.02685  32.984  < 2e-16 ***
## a      1.07937    0.36028   2.996  0.00274 ** 
## b      3.52854    0.36094   9.776  < 2e-16 ***
## c     18.62841    0.50436  36.935  < 2e-16 ***
## d      1.90401    0.16277  11.697  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6474 on 7672 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (112 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 60 rows containing missing values (`geom_point()`).

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7807     5112.9                                
## 2   7806     4675.8  1  437.1  729.71 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 39574.71
## 2     2 38878.58
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.68024    0.26003   6.462  1.1e-10 ***
## alpha  0.86337    0.02851  30.287  < 2e-16 ***
## a      2.12476    0.16290  13.044  < 2e-16 ***
## b      2.07094    0.15293  13.541  < 2e-16 ***
## c     17.38074    0.65206  26.655  < 2e-16 ***
## d      1.25393    0.10522  11.918  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.774 on 7806 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (128 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 63 rows containing missing values (`geom_point()`).

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)    
## 1    802     465.89                               
## 2    801     437.60  1 28.288  51.778 1.43e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4064.862
## 2     2 4016.313
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.68067    0.73953   0.920 0.357638    
## alpha  0.79965    0.09996   7.999 4.37e-15 ***
## a      3.02218    0.63011   4.796 1.93e-06 ***
## b      2.13229    0.57374   3.716 0.000216 ***
## c     21.44192    3.43187   6.248 6.75e-10 ***
## d      0.91822    0.33809   2.716 0.006752 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7391 on 801 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (23 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 8 rows containing missing values (`geom_point()`).

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    976     333.50                              
## 2    975     329.85  1 3.6469   10.78 0.001063 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3706.157
## 2     2 3697.370
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.2660     0.4874   0.546 0.585312    
## alpha   0.4179     0.1217   3.435 0.000617 ***
## a       0.0000     5.3686   0.000 1.000000    
## b       2.8573     5.3800   0.531 0.595476    
## c      26.7202     9.6781   2.761 0.005873 ** 
## d       3.5196     4.4523   0.791 0.429422    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5816 on 975 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (411 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 224 rows containing missing values (`geom_point()`).
## Warning: Removed 1 rows containing missing values (`geom_segment()`).

plotting 2

## Warning: Removed 1 rows containing missing values (`geom_segment()`).

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    420     832.94                            
## 2    419     825.85  1 7.0966  3.6005 0.05845 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2318.893
## 2     2 2317.256
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     1.1889     2.0929   0.568  0.57030    
## alpha   0.6203     0.3008   2.062  0.03984 *  
## a       0.0000     1.1030   0.000  1.00000    
## b       3.5531     1.6428   2.163  0.03112 *  
## c      18.6079     2.9988   6.205 1.31e-09 ***
## d       1.3099     0.4895   2.676  0.00774 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.404 on 419 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (19 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 10 rows containing missing values (`geom_point()`).

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

322 - American Semidesert and Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

331 - Great Plains/Palouse Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

332 - Great Plains Steppe

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

341 - Intermountain Semi-desert & Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

342 - Intermountain Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5090     1413.3                                
## 2   5089     1338.2  1 75.173  285.88 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 19343.53
## 2     2 19067.06
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.09007    0.24656   4.421    1e-05 ***
## alpha  0.63616    0.03509  18.127   <2e-16 ***
## a      0.97615    1.26167   0.774   0.4391    
## b      1.95500    1.24894   1.565   0.1176    
## c     34.19072    2.32877  14.682   <2e-16 ***
## d      2.20422    0.90326   2.440   0.0147 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5128 on 5089 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (13 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 7 rows containing missing values (`geom_point()`).

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5154     2644.7                                
## 2   5153     2580.9  1 63.714  127.21 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 24436.20
## 2     2 24312.39
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.88368    0.25792   3.426 0.000617 ***
## alpha  0.81056    0.06798  11.923  < 2e-16 ***
## a      1.86507    0.58588   3.183 0.001464 ** 
## b      2.08079    0.55574   3.744 0.000183 ***
## c     27.63128    2.24333  12.317  < 2e-16 ***
## d      1.51203    0.36801   4.109 4.04e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7077 on 5153 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (27 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 14 rows containing missing values (`geom_point()`).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    594     360.14                                
## 2    593     349.15  1  10.99  18.666 1.826e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2541.955
## 2     2 2525.391
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     3.2969     1.7985   1.833 0.067280 .  
## alpha   0.9650     0.2059   4.686 3.45e-06 ***
## a       1.4792     0.3538   4.181 3.34e-05 ***
## b       1.2132     0.4566   2.657 0.008094 ** 
## c      30.4913     2.7871  10.940  < 2e-16 ***
## d       0.4209     0.1126   3.736 0.000205 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7673 on 593 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 1 rows containing missing values (`geom_point()`).

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    672     368.32                                
## 2    671     349.67  1 18.647  35.783 3.587e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2860.020
## 2     2 2826.847
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     5.0000     2.7919   1.791 0.073756 .  
## alpha   0.9432     0.1463   6.445 2.21e-10 ***
## a       1.3379     0.3993   3.351 0.000852 ***
## b       0.7534     0.8698   0.866 0.386754    
## c       5.7656    10.3109   0.559 0.576226    
## d       1.1578     1.2049   0.961 0.336943    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7219 on 671 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 3 rows containing missing values (`geom_point()`).

plotting 2

M242 - Cascade Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M262 - California Coastal Range = Coniferous Forest - Open woodland Shrub Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    210     220.84                                
## 2    209     208.75  1 12.085  12.099 0.0006136 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 714.2646
## 2     2 704.1649
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.1264     1.6830  -0.075 0.940186    
## alpha   0.8046     0.2067   3.893 0.000133 ***
## a       0.0000    14.2323   0.000 1.000000    
## b       1.4399    14.2300   0.101 0.919497    
## c      71.0209    27.5153   2.581 0.010532 *  
## d       1.8423    11.1488   0.165 0.868910    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9994 on 209 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (91 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 47 rows containing missing values (`geom_point()`).
## Warning: Removed 2 rows containing missing values (`geom_point()`).
## Warning: Removed 2 rows containing missing values (`geom_pointrange()`).

plotting 2

## Warning: Removed 2 rows containing missing values (`geom_point()`).
## Warning: Removed 2 rows containing missing values (`geom_pointrange()`).

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest 2
212 Laurentian Mixed Forest 2
221 Eastern Broadleaf Forest 2
222 Midwest Broadleaf Forest 2
223 Central Interior Broadleaf Forest 2
231 Southeastern Mixed Forest 2
232 Outer Coastal Plain Mixed Forest 2
234 Lower Mississippi Riverine Forest 2
242 Pacific Lowland Mixed Forest NA
251 Prairie Parkland (Temperate) 2
255 Prairie Parkland (Subtropical) 2
261 California Coastal Chaparral Forest and Shrub NA
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA
313 Colorado Plateau Semi-Desert NA
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert NA
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe NA
332 Great Plains Steppe NA
341 Intermountain Semi-Desert and Desert NA
342 Intermountain Semi-Desert NA
411 Everglades NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 2
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 2
M223 Ozark Broadleaf Forest Meadow 2
M231 Ouachita Mixed Forest 2
M242 Cascade Mixed Forest NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow NA
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA
M334 Black Hills Coniferous Forest 2
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA

table by ecoprovince

Code Ecoregion region n.obs n.plots tau tau.variance tau.2.5 tau.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 a a.2.5 a.97.5 b b.2.5 b.97.5 c c.2.5 c.97.5 d d.2.5 d.97.5
211 Northeastern Mixed Forest east 4838 2419 0.2407307 0.0318940 -0.1093852 0.5908466 0.6366052 0.0016727 0.5564260 0.7167845 0.0000000 -3.2764180 3.2764180 3.4218034 0.1603849 6.683222 35.421923 31.212391 39.63145 2.5909373 1.0289425 4.1529320
212 Laurentian Mixed Forest east 12962 6481 1.2834957 0.0461109 0.8625717 1.7044197 0.7967510 0.0007875 0.7417423 0.8517598 0.3319524 -0.2108728 0.8747776 2.0401034 1.4905122 2.589694 24.654288 22.973222 26.33536 2.3882279 1.8971604 2.8792954
221 Eastern Broadleaf Forest east 5446 2723 -0.3615051 0.0265069 -0.6806771 -0.0423331 0.7029289 0.0021203 0.6126581 0.7931997 0.0000000 -4.1877168 4.1877168 4.3157517 0.1274891 8.504014 38.220365 32.649930 43.79080 2.7196661 1.0003695 4.4389626
222 Midwest Broadleaf Forest east 3552 1776 0.1932761 0.0754170 -0.3452113 0.7317634 0.8268602 0.0028308 0.7225328 0.9311876 1.3211293 0.3705391 2.2717194 2.0413216 1.0871790 2.995464 48.174412 40.034159 56.31466 1.9754729 1.1582391 2.7927066
223 Central Interior Broadleaf Forest east 6388 3194 -0.5104308 0.0211344 -0.7954297 -0.2254320 0.5780045 0.0025614 0.4787870 0.6772220 2.4465926 1.7207101 3.1724750 1.5643357 0.8519575 2.276714 31.402667 26.435818 36.36952 1.2770141 0.7318236 1.8222047
231 Southeastern Mixed Forest east 7790 3895 1.5275075 0.0434045 1.1191091 1.9359059 0.8854662 0.0007207 0.8328416 0.9380908 1.0793663 0.3731250 1.7856076 3.5285383 2.8210030 4.236073 18.628410 17.639721 19.61710 1.9040140 1.5849329 2.2230951
232 Outer Coastal Plain Mixed Forest east 7940 3970 1.6802446 0.0676175 1.1705090 2.1899802 0.8633743 0.0008126 0.8074945 0.9192540 2.1247568 1.8054350 2.4440785 2.0709394 1.7711461 2.370733 17.380742 16.102525 18.65896 1.2539274 1.0476777 1.4601771
234 Lower Mississippi Riverine Forest east 830 415 0.6806672 0.5469034 -0.7709769 2.1323112 0.7996511 0.0099926 0.6034306 0.9958717 3.0221780 1.7853184 4.2590376 2.1322889 1.0060814 3.258496 21.441924 14.705397 28.17845 0.9182159 0.2545666 1.5818652
242 Pacific Lowland Mixed Forest west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
251 Prairie Parkland (Temperate) east 1392 696 0.2660455 0.2375785 -0.6904679 1.2225590 0.4179242 0.0148020 0.1791720 0.6566764 0.0000000 -10.5352527 10.5352527 2.8572644 -7.7004058 13.414935 26.720218 7.727881 45.71255 3.5195623 -5.2175709 12.2566956
255 Prairie Parkland (Subtropical) east 444 222 1.1888589 4.3801029 -2.9249730 5.3026908 0.6203062 0.0905101 0.0289451 1.2116674 0.0000000 -2.1681198 2.1681198 3.5531088 0.3239081 6.782310 18.607909 12.713432 24.50239 1.3099428 0.3477800 2.2721056
261 California Coastal Chaparral Forest and Shrub west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest west 4 2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe west 118 59 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe west 154 77 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
341 Intermountain Semi-Desert and Desert west 4 2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert west 2 1 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
411 Everglades east 66 33 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 5108 2554 1.0900669 0.0607930 0.6066987 1.5734351 0.6361575 0.0012316 0.5673578 0.7049571 0.9761451 -1.4972711 3.4495613 1.9550016 -0.4934585 4.403462 34.190718 29.625330 38.75611 2.2042212 0.4334392 3.9750031
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 5186 2593 0.8836790 0.0665226 0.3780468 1.3893112 0.8105585 0.0046215 0.6772863 0.9438308 1.8650716 0.7165000 3.0136432 2.0807897 0.9913069 3.170273 27.631280 23.233399 32.02916 1.5120304 0.7905689 2.2334920
M223 Ozark Broadleaf Forest Meadow east 602 301 3.2968837 3.2344864 -0.2352575 6.8290250 0.9649685 0.0424011 0.5605566 1.3693804 1.4791696 0.7843063 2.1740329 1.2131708 0.3164662 2.109875 30.491278 25.017567 35.96499 0.4208667 0.1996297 0.6421037
M231 Ouachita Mixed Forest east 680 340 5.0000000 7.7944526 -0.4818226 10.4818226 NA NA NA NA 1.3378653 0.5538449 2.1218857 0.7533553 -0.9545851 2.461296 5.765626 -14.479809 26.01106 1.1577725 -1.2079946 3.5235396
M242 Cascade Mixed Forest west 34 17 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow west 330 165 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow west 8 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow west 20 10 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow west 22 11 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M334 Black Hills Coniferous Forest west 306 153 -0.1264331 2.8323248 -3.4441686 3.1913023 0.8046391 0.0427282 0.3971392 1.2121389 0.0000000 -28.0572665 28.0572665 1.4399205 -26.6127698 29.492611 71.020853 16.777839 125.26387 1.8422905 -20.1361523 23.8207333
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

plot tau

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I
## Warning: package 'ggnewscale' was built under R version 4.2.1
## Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
## ℹ Please use tidy evaluation ideoms with `aes()`
## Warning: The `size` argument of `element_line()` is deprecated as of ggplot2 3.4.0.
## ℹ Please use the `linewidth` argument instead.
## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

plot alpha (biomass growth compensation effect)

plot a coefficient

## Warning: Removed 21 rows containing missing values (`geom_point()`).

plot b coefficient

## Warning: Removed 21 rows containing missing values (`geom_point()`).

plot c coefficient

## Warning: Removed 1 rows containing missing values (`geom_hline()`).
## Warning: Removed 22 rows containing missing values (`geom_point()`).

plot d coefficient

## Warning: Removed 21 rows containing missing values (`geom_point()`).


Analysis 2: No-harvest

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4729     1518.4                                
## 2   4728     1497.6  1  20.77  65.572 7.066e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 18976.29
## 2     2 18913.09
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.55154    0.24459   2.255  0.02418 *  
## alpha  0.69380    0.08191   8.471  < 2e-16 ***
## a      0.00000    1.89752   0.000  1.00000    
## b      3.29975    1.88697   1.749  0.08041 .  
## c     32.96538    1.92687  17.108  < 2e-16 ***
## d      2.48730    0.88804   2.801  0.00512 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5628 on 4728 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (38 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 18 rows containing missing values (`geom_point()`).

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  14324     6454.5                                
## 2  14323     6353.0  1 101.41  228.63 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 52899.90
## 2     2 52674.98
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     1.1876     0.1970   6.028  1.7e-09 ***
## alpha   0.6832     0.0429  15.926  < 2e-16 ***
## a       0.5003     0.1918   2.609   0.0091 ** 
## b       1.8381     0.1949   9.433  < 2e-16 ***
## c      25.3009     0.7774  32.546  < 2e-16 ***
## d       2.0440     0.1709  11.960  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.666 on 14323 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2821 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 1382 rows containing missing values (`geom_point()`).

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5737     2245.5                                
## 2   5736     2212.0  1 33.502  86.877 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 25703.92
## 2     2 25619.61
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.49211    0.16644  -2.957 0.003123 ** 
## alpha  0.70784    0.07268   9.740  < 2e-16 ***
## a      0.00000    1.72362   0.000 1.000000    
## b      4.43677    1.72532   2.572 0.010149 *  
## c     39.60558    2.44144  16.222  < 2e-16 ***
## d      2.56369    0.66008   3.884 0.000104 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.621 on 5736 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (60 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 25 rows containing missing values (`geom_point()`).

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3581     1455.3                                
## 2   3580     1418.9  1 36.397  91.835 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 14852.55
## 2     2 14763.72
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.02831    0.26269   0.108    0.914    
## alpha  0.71160    0.06935  10.262  < 2e-16 ***
## a      1.46035    0.28196   5.179 2.35e-07 ***
## b      1.91589    0.28501   6.722 2.08e-11 ***
## c     49.13281    3.10887  15.804  < 2e-16 ***
## d      1.64185    0.25033   6.559 6.21e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6295 on 3580 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (778 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 399 rows containing missing values (`geom_point()`).

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6509     2848.8                                
## 2   6508     2833.4  1  15.37  35.303 2.968e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 27147.39
## 2     2 27114.15
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.08251    0.18363  -0.449    0.653    
## alpha  0.47117    0.07678   6.137 8.92e-10 ***
## a      2.05466    0.31852   6.451 1.19e-10 ***
## b      1.45558    0.30703   4.741 2.17e-06 ***
## c     30.27754    1.93150  15.676  < 2e-16 ***
## d      1.25297    0.24567   5.100 3.49e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6598 on 6508 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (917 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 454 rows containing missing values (`geom_point()`).

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   9054     3797.3                                
## 2   9053     3739.5  1 57.813  139.96 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 44842.09
## 2     2 44705.11
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.66023    0.22625   7.338 2.35e-13 ***
## alpha  0.70251    0.05668  12.395  < 2e-16 ***
## a      0.78181    0.40500   1.930   0.0536 .  
## b      3.64805    0.40329   9.046  < 2e-16 ***
## c     18.56009    0.45842  40.487  < 2e-16 ***
## d      1.99852    0.17717  11.280  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6427 on 9053 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (208 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 115 rows containing missing values (`geom_point()`).

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   9259     5381.4                                
## 2   9258     5279.2  1 102.13  179.11 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 46596.17
## 2     2 46420.66
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    2.21576    0.30934   7.163 8.51e-13 ***
## alpha  0.67027    0.04732  14.165  < 2e-16 ***
## a      2.14561    0.12609  17.016  < 2e-16 ***
## b      1.79345    0.11498  15.598  < 2e-16 ***
## c     16.78133    0.59405  28.249  < 2e-16 ***
## d      1.08028    0.07988  13.524  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7551 on 9258 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (242 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 122 rows containing missing values (`geom_point()`).

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1042     611.60                                
## 2   1041     599.54  1 12.069  20.956 5.265e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 5298.024
## 2     2 5279.156
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     1.3150     0.9674   1.359   0.1744    
## alpha   0.7081     0.1446   4.897 1.13e-06 ***
## a       1.3185     1.5881   0.830   0.4066    
## b       2.6224     1.6247   1.614   0.1068    
## c      23.8752     2.9088   8.208 6.60e-16 ***
## d       1.7062     0.8197   2.081   0.0376 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7589 on 1041 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (48 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 26 rows containing missing values (`geom_point()`).

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1   1461     562.19                              
## 2   1460     558.07  1  4.119  10.776 0.001053 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 5678.475
## 2     2 5669.694
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.6718     0.5104   1.316 0.188317    
## alpha   0.4223     0.1238   3.412 0.000663 ***
## a       0.0000    10.9656   0.000 1.000000    
## b       2.6048    10.9674   0.238 0.812299    
## c      23.9322     8.5379   2.803 0.005129 ** 
## d       4.1766    10.1509   0.411 0.680798    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6183 on 1460 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (424 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 200 rows containing missing values (`geom_point()`).

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    594     658.24                                
## 2    593     642.29  1 15.944   14.72 0.0001381 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2860.289
## 2     2 2847.601
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.6581     1.1908   0.553  0.58072    
## alpha   0.7760     0.1828   4.244 2.54e-05 ***
## a       0.4340     0.9627   0.451  0.65224    
## b       3.0156     1.1074   2.723  0.00666 ** 
## c      20.1594     1.8401  10.955  < 2e-16 ***
## d       1.3486     0.4194   3.215  0.00137 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.041 on 593 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (39 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 17 rows containing missing values (`geom_point()`).

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

322 - American Semidesert and Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

331 - Great Plains/Palouse Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

332 - Great Plains Steppe

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

341 - Intermountain Semi-desert & Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

342 - Intermountain Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4816     1171.2                                
## 2   4815     1164.7  1 6.5683  27.155 1.956e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 17976.22
## 2     2 17951.11
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.40024    0.30134   4.647 3.46e-06 ***
## alpha  0.42865    0.07987   5.367 8.40e-08 ***
## a      2.28094    0.14232  16.026  < 2e-16 ***
## b      0.60899    0.08256   7.376 1.91e-13 ***
## c     30.49218    1.98928  15.328  < 2e-16 ***
## d      0.82574    0.15904   5.192 2.16e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4918 on 4815 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (17 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 11 rows containing missing values (`geom_point()`).

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7147     3539.6                                
## 2   7146     3503.8  1 35.789  72.993 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 33643.11
## 2     2 33572.43
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.06286    0.25268   4.206 2.63e-05 ***
## alpha  0.77819    0.08733   8.911  < 2e-16 ***
## a      2.32857    0.27855   8.360  < 2e-16 ***
## b      1.46884    0.23819   6.167 7.35e-10 ***
## c     27.60317    1.99164  13.860  < 2e-16 ***
## d      1.18770    0.22998   5.164 2.48e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7002 on 7146 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (49 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 25 rows containing missing values (`geom_point()`).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)  
## 1    745     434.35                           
## 2    744     430.81  1 3.5355  6.1057 0.0137 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model     AIC
## 1     1 3139.42
## 2     2 3135.29
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    3.26781    1.84192   1.774 0.076451 .  
## alpha  0.67407    0.25821   2.611 0.009221 ** 
## a      1.47179    0.34957   4.210 2.86e-05 ***
## b      1.05698    0.40303   2.623 0.008906 ** 
## c     38.69332    2.29566  16.855  < 2e-16 ***
## d      0.25262    0.07175   3.521 0.000457 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.761 on 744 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (5 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 2 rows containing missing values (`geom_point()`).

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)   
## 1    828     428.21                             
## 2    827     424.53  1 3.6794  7.1676 0.00757 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3518.799
## 2     2 3513.610
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    4.40938    2.45305   1.798 0.072620 .  
## alpha  0.72488    0.25928   2.796 0.005298 ** 
## a      1.37715    0.37605   3.662 0.000266 ***
## b      0.90911    0.32986   2.756 0.005980 ** 
## c     26.09391    2.05779  12.681  < 2e-16 ***
## d      0.35507    0.09332   3.805 0.000152 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7165 on 827 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (7 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 2 rows containing missing values (`geom_point()`).

plotting 2

M242 - Cascade Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3092     2835.8                                
## 2   3091     2741.6  1 94.182  106.19 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 16937.51
## 2     2 16834.90
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -1.64465    0.29716  -5.535 3.38e-08 ***
## alpha  0.99393    0.08794  11.302  < 2e-16 ***
## a      6.14292    0.58908  10.428  < 2e-16 ***
## b      4.58403    0.90943   5.041 4.91e-07 ***
## c     34.94264    1.72143  20.299  < 2e-16 ***
## d      0.31656    0.06078   5.208 2.03e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9418 on 3091 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (75 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 42 rows containing missing values (`geom_point()`).

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1590     1542.8                                
## 2   1589     1523.8  1 19.044  19.859 8.921e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 8275.762
## 2     2 8257.951
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -2.5413     0.2376 -10.698  < 2e-16 ***
## alpha   0.6625     0.1395   4.748 2.24e-06 ***
## a       0.0000     1.8821   0.000        1    
## b       8.0988     2.0030   4.043 5.52e-05 ***
## c      56.8554     6.3381   8.970  < 2e-16 ***
## d       2.4290     0.4874   4.984 6.91e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9793 on 1589 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (284 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 151 rows containing missing values (`geom_point()`).

plotting 2

M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    333     169.21                                
## 2    332     163.63  1 5.5875  11.337 0.0008489 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 955.5906
## 2     2 946.2412
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -2.5474     0.3050  -8.353 1.84e-15 ***
## alpha   0.5795     0.1606   3.608 0.000356 ***
## a       0.0000     5.3207   0.000 1.000000    
## b       3.4586     5.3738   0.644 0.520276    
## c      61.8314    18.5603   3.331 0.000962 ***
## d       2.0674     2.3333   0.886 0.376248    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.702 on 332 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1684     1572.6                                
## 2   1683     1517.5  1 55.033  61.033 9.807e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 5100.938
## 2     2 5042.772
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.92798    0.59404  -1.562 0.118440    
## alpha  0.60538    0.06795   8.909  < 2e-16 ***
## a      0.06516    0.69480   0.094 0.925295    
## b      1.92757    0.73647   2.617 0.008942 ** 
## c     49.63328    3.62429  13.695  < 2e-16 ***
## d      1.98777    0.55580   3.576 0.000358 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9496 on 1683 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (29 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 12 rows containing missing values (`geom_point()`).

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

##   model      AIC
## 1     1 739.3605
## 2     2 734.0836
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     1.1798     2.5654   0.460  0.64601    
## alpha   0.7234     0.2525   2.865  0.00455 ** 
## a       0.0000     0.7983   0.000  1.00000    
## b       1.0855     0.8564   1.268  0.20621    
## c      84.8244    16.8490   5.034 9.54e-07 ***
## d       1.4393     1.1099   1.297  0.19599    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9014 on 235 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (75 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

predict and plot

## Warning: Removed 36 rows containing missing values (`geom_point()`).
## Warning: Removed 1 rows containing missing values (`geom_segment()`).

plotting 2

## Warning: Removed 1 rows containing missing values (`geom_segment()`).

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest 2
212 Laurentian Mixed Forest 2
221 Eastern Broadleaf Forest 2
222 Midwest Broadleaf Forest 2
223 Central Interior Broadleaf Forest 2
231 Southeastern Mixed Forest 2
232 Outer Coastal Plain Mixed Forest 2
234 Lower Mississippi Riverine Forest 2
242 Pacific Lowland Mixed Forest NA
251 Prairie Parkland (Temperate) 2
255 Prairie Parkland (Subtropical) 2
261 California Coastal Chaparral Forest and Shrub NA
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA
313 Colorado Plateau Semi-Desert NA
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert NA
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe NA
332 Great Plains Steppe NA
341 Intermountain Semi-Desert and Desert NA
342 Intermountain Semi-Desert NA
411 Everglades NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 2
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 2
M223 Ozark Broadleaf Forest Meadow 2
M231 Ouachita Mixed Forest 2
M242 Cascade Mixed Forest 2
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 2
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow 2
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow 2
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA
M334 Black Hills Coniferous Forest 2
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA

table by ecoprovince

Code Ecoregion region n.obs n.plots tau tau.variance tau.2.5 tau.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 a a.2.5 a.97.5 b b.2.5 b.97.5 c c.2.5 c.97.5 d d.2.5 d.97.5
211 Northeastern Mixed Forest east 4838 2419 0.5515401 0.0598257 0.0720238 1.0310563 0.6938024 0.0067087 0.5332269 0.8543779 0.0000000 -3.7200270 3.7200270 3.2997501 -0.3995932 6.999093 32.96538 29.187819 36.74294 2.4873010 0.7463258 4.2282762
212 Laurentian Mixed Forest east 12962 6481 1.1876148 0.0388168 0.8014307 1.5737990 0.6832251 0.0018405 0.5991330 0.7673172 0.5002676 0.1243505 0.8761848 1.8381506 1.4561975 2.220104 25.30091 23.777144 26.82467 2.0439510 1.7089602 2.3789417
221 Eastern Broadleaf Forest east 5446 2723 -0.4921082 0.0277038 -0.8184022 -0.1658141 0.7078374 0.0052819 0.5653631 0.8503117 0.0000000 -3.3789373 3.3789373 4.4367692 1.0544933 7.819045 39.60558 34.819439 44.39172 2.5636857 1.2696859 3.8576854
222 Midwest Broadleaf Forest east 3552 1776 0.0283094 0.0690062 -0.4867282 0.5433471 0.7115958 0.0048089 0.5756342 0.8475575 1.4603509 0.9075423 2.0131595 1.9158937 1.3570908 2.474697 49.13281 43.037470 55.22816 1.6418451 1.1510428 2.1326474
223 Central Interior Broadleaf Forest east 6388 3194 -0.0825059 0.0337210 -0.4424867 0.2774749 0.4711714 0.0058952 0.3206570 0.6216858 2.0546598 1.4302502 2.6790695 1.4555816 0.8537029 2.057460 30.27754 26.491161 34.06392 1.2529688 0.7713709 1.7345668
231 Southeastern Mixed Forest east 7790 3895 1.6602295 0.0511891 1.2167283 2.1037306 0.7025126 0.0032122 0.5914139 0.8136113 0.7818095 -0.0120881 1.5757072 3.6480498 2.8575020 4.438598 18.56009 17.661479 19.45871 1.9985204 1.6512194 2.3458214
232 Outer Coastal Plain Mixed Forest east 7940 3970 2.2157636 0.0956924 1.6093853 2.8221419 0.6702732 0.0022390 0.5775188 0.7630276 2.1456073 1.8984365 2.3927782 1.7934510 1.5680713 2.018831 16.78133 15.616858 17.94581 1.0802794 0.9237045 1.2368542
234 Lower Mississippi Riverine Forest east 830 415 1.3149574 0.9358533 -0.5833092 3.2132239 0.7080513 0.0209036 0.4243483 0.9917543 1.3184695 -1.7978464 4.4347854 2.6224194 -0.5655835 5.810422 23.87516 18.167400 29.58293 1.7061821 0.0977380 3.3146262
242 Pacific Lowland Mixed Forest west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
251 Prairie Parkland (Temperate) east 1392 696 0.6718225 0.2605392 -0.3294327 1.6730777 0.4222983 0.0153194 0.1795090 0.6650876 0.0000000 -21.5100523 21.5100523 2.6048063 -18.9087722 24.118385 23.93220 7.184283 40.68012 4.1766358 -15.7351727 24.0884444
255 Prairie Parkland (Subtropical) east 444 222 0.6581040 1.4181111 -1.6806823 2.9968902 0.7759632 0.0334229 0.4169113 1.1350151 0.4340458 -1.4565741 2.3246656 3.0155967 0.8407385 5.190455 20.15935 16.545353 23.77335 1.3486419 0.5248783 2.1724055
261 California Coastal Chaparral Forest and Shrub west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest west 4 2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe west 118 59 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe west 154 77 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
341 Intermountain Semi-Desert and Desert west 4 2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert west 2 1 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
411 Everglades east 66 33 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 5108 2554 1.4002378 0.0908084 0.8094653 1.9910102 0.4286478 0.0063798 0.2720584 0.5852372 2.2809388 2.0019204 2.5599572 0.6089923 0.4471307 0.770854 30.49218 26.592285 34.39207 0.8257441 0.5139626 1.1375257
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 5186 2593 1.0628617 0.0638472 0.5675339 1.5581895 0.7781929 0.0076257 0.6070096 0.9493762 2.3285740 1.7825423 2.8746056 1.4688405 1.0019195 1.935762 27.60317 23.698964 31.50738 1.1877006 0.7368730 1.6385281
M223 Ozark Broadleaf Forest Meadow east 602 301 3.2678069 3.3926776 -0.3481769 6.8837906 0.6740728 NA 0.1671705 1.1809751 1.4717897 0.7855302 2.1580491 1.0569808 0.2657631 1.848198 38.69332 34.186590 43.20006 0.2526235 0.1117624 0.3934845
M231 Ouachita Mixed Forest east 680 340 4.4093816 6.0174665 -0.4055597 9.2243229 0.7248842 NA 0.2159590 1.2338095 1.3771528 0.6390356 2.1152700 0.9091071 0.2616430 1.556571 26.09391 22.054798 30.13302 0.3550674 0.1718922 0.5382426
M242 Cascade Mixed Forest west 34 17 -1.6446455 0.0883049 -2.2272992 -1.0619918 0.9939271 0.0077335 0.8214992 1.1663550 6.1429172 4.9878885 7.2979458 4.5840263 2.8008839 6.367169 34.94264 31.567382 38.31790 0.3165643 0.1973925 0.4357361
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow west 330 165 -2.5412962 0.0564305 -3.0072428 -2.0753496 0.6625148 0.0194689 0.3888307 0.9361990 0.0000000 -3.6915653 3.6915653 8.0988192 4.1700612 12.027577 56.85542 44.423410 69.28743 2.4290362 1.4730733 3.3849991
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow west 8 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow west 0 0 -2.5473810 0.0930135 -3.1473200 -1.9474420 0.5794630 0.0257880 0.2635677 0.8953584 0.0000000 -10.4665460 10.4665460 3.4586229 -7.1124288 14.029675 61.83144 25.320750 98.34214 2.0673628 -2.5225764 6.6573021
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow west 0 0 -0.9279839 0.3528855 -2.0931221 0.2371543 0.6053802 0.0046175 0.4721003 0.7386601 0.0651589 -1.2976134 1.4279313 1.9275747 0.4830820 3.372067 49.63328 42.524697 56.74187 1.9877692 0.8976330 3.0779055
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow west 20 10 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow west 22 11 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M334 Black Hills Coniferous Forest west 306 153 1.1798413 6.5812153 -3.8742553 6.2339379 0.7234150 0.0637650 0.2259281 1.2209019 0.0000000 -1.5726990 1.5726990 1.0854718 -0.6016339 2.772578 84.82438 51.629969 118.01878 1.4392864 -0.7474002 3.6259729
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

plot tau

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

plot alpha (biomass growth compensation effect)

plot a coefficient

## Warning: Removed 17 rows containing missing values (`geom_point()`).

plot b coefficient

## Warning: Removed 17 rows containing missing values (`geom_point()`).

plot c coefficient

## Warning: Removed 1 rows containing missing values (`geom_hline()`).
## Warning: Removed 18 rows containing missing values (`geom_point()`).

plot d coefficient

## Warning: Removed 17 rows containing missing values (`geom_point()`).